I was having this particular problem off and on when using Mac OS X Mail on my work Mac, which was set up to use our corporate exchange server, and an 'Exchange 2007' Mail account: Every so often, Mail would quit getting new messages in the inbox, and when I checked the 'Activity' window, I would get the following error:
(Screenshot to be posted here)
("Opening Mailbox — Requesting Latest Information")
Sometimes, simply hitting the 'stop sign' would allow me to get new messages, but the problem would always crop up again. Other times, I'd pull out my Mac laptop, which was set up to use IMAP instead of Exchange (long story, details don't matter), and after syncing it up with the server, and restarting Mail on my main Mac, the problem would go away.
Only today, after finding this forum thread on Apple's Discussion Forums, did I find the source of the problem: